In Sec. REF , we argue the effect of accretion based on the calculation in Ref. [1]}. We propose to split the life of each mode into different phases. The life of every mode has at least three phases: accelerating, decelerating, and attractor phases. The dominant mode may also have a quasi-normal phase if accretion is efficient. With this splitting strategy, the analysis of BH-condensate evolution with an arbitrary number of modes is much simplified. In Sec. REF , we argue the scalar self-interaction does not shut down the \(\lbrace 1,1,1\rbrace \)  mode.
